In this paper, we prove that the five-dimensional Schwarzschild- Tangherlini solution of the Einstein vacuum equations is orbitally stable (in the fully non-linear theory) with respect to vacuum perturbations of initial data preserving triaxial Bianchi-IX symmetry. More generally, we prove that five-dimensional vacuum spacetimes developing from suitable asymptotically flat triaxial Bianchi-IX symmetric initial data and containing a trapped or marginally trapped homogeneous 3-surface necessarily possess a complete null infinity I+, whose past J-(I+) is bounded to the future by a regular event horizon H+, whose cross-sectional volume in turn satisfies a Penrose inequality, relating it to the final Bondi mass. In particular, the results of this paper give the first examples of vacuum black holes which are not stationary exact solutions.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)